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Characterizations of regular local rings in positive characteristics


Author: Jinjia Li
Journal: Proc. Amer. Math. Soc. 136 (2008), 1553-1558
MSC (2000): Primary 13A35, 13D07, 13D25, 13H05.
DOI: https://doi.org/10.1090/S0002-9939-07-09158-7
Published electronically: November 23, 2007
MathSciNet review: 2373583
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Abstract: In this note, we provide several characterizations of regular local rings in positive characteristics, in terms of the Hilbert-Kunz multiplicity and its higher $ \mathrm{Tor}$ counterparts $ {\mathfrak{i}} t_i={\lim}_{n \to \infty} \ell(\mathrm{Tor}_i(k,{}^{f^n} R))/p^{nd}$. We also apply the characterizations to improve a recent result by Bridgeland and Iyengar in the characteristic $ p$ case. Our proof avoids using the existence of big Cohen-Macaulay modules, which is the major tool in the proof of Bridgeland and Iyengar.


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Additional Information

Jinjia Li
Affiliation: Department of Mathematics, Syracuse University, 215 Carnegie, Syracuse, New York 13244
Email: jli32@syr.edu

DOI: https://doi.org/10.1090/S0002-9939-07-09158-7
Keywords: Regular local ring, Hilbert-Kunz multiplicity, Frobenius, Tor
Received by editor(s): December 1, 2006
Received by editor(s) in revised form: February 19, 2007
Published electronically: November 23, 2007
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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